Review Problems for Introductory Physics 1

[Pages:608]Review Problems for

Introductory Physics 1

May 20, 2019 Robert G. Brown, Instructor Duke University Physics Department

Durham, NC 27708-0305 rgb@phy.duke.edu

Copyright Notice

This document is Copyright Robert G. Brown 2011. The specific date of last modification is determinable by examining the original document sources.

Contents

1 Preface

3

2 Short Math Review Problems

5

2.0.1 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Essential Laws, Theorems, and Principles

21

4 Problem Solving

27

5 Newton's Laws

29

5.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.1.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.1.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3 Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.3.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6 Work and Energy

123

6.1 Work and Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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6.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.2 Work and Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.2.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.2.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6.2.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.2.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.3.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.3.2 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

7 Center of Mass and Momentum

175

7.1 Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

7.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

7.1.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

7.1.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.2.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.2.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

7.2.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

8 One Dimensional Rotation and Torque

229

8.1 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

8.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

8.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

8.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

8.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

8.2 Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

8.2.1 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

8.2.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

8.2.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

9 Vector Torque and Angular Momentum

289

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9.1 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 9.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 9.1.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 9.1.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

9.2 Vector Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 9.2.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 9.2.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 9.2.3 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

10 Statics

323

10.1 Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

10.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

10.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

10.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

10.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

11 Fluids

379

11.1 Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

11.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

11.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

11.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

11.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

12 Oscillations

451

12.1 Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

12.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

12.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

12.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

12.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

13 Waves

513

13.1 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

13.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

13.1.2 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

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13.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 13.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

14 Sound

537

14.1 Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

14.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

14.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

14.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

14.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

15 Gravity

569

15.1 Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

15.1.1 Multiple Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

15.1.2 Ranking/Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577

15.1.3 Short Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578

15.1.4 Long Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

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Chapter 1

Preface

The problems in this review guide are provided as is without any guarantee of being correct! That's not to suggest that they are all broken ? on the contrary, most of them are well-tested and have been used as homework, quiz and exam problems for decades if not centuries. It is to suggest that they have typos in them, errors of other sorts, bad figures, and one or two of them are really too difficult for this course but haven't been sorted out or altered to make them doable.

Leaving these in just adds to the fun. Physics problems are not all cut and dried; physics itself isn't. One thing you should be building up as you work is an appreciation for what is easy, what is difficult, what is correct and what is incorrect. If you find an error and bring it to my attention, I'll do my best to correct it, of course, but in the meantime, be warned!

A few of the problems have rather detailed solutions (due to Prof. Ronen Plesser and myself), provided as examples of how a really good solution might develop, with considerable annotation. However, most problems do not have included solutions and never will have. I am actually philosophically opposed to providing students with solutions that they are then immediately tempted to memorize. This guide is provided so that you can learn to solve problems and work sufficiently carefully that they can trust the solutions.

Students invariably then ask: But how are we to know if we've solved the problems correctly?"

The answer is simple. The same way you would in the real world! Work on them in groups and check your algebra, your approach, and your answers against one another's. Build a consensus. Solve them with mentoring (course TAs, professors, former students, tutors all are happy to help you). Find answers through research on the web or in the literature.

To be honest, almost any of the ways that involve hard work on your part are good ways to learn to solve physics problems. The only bad way to (try to) learn is to have the material all laid out, cut and dried, so that you don't have to struggle to learn, so that you don't have to work hard and thereby permanently imprint the knowledge on your brain as you go. Physics requires engagement and investment of time and energy like no subject you have ever taken, if only because it is one of the most difficult subjects you've ever tried to learn (at the same time it is remarkably simple, paradoxically enough).

In any event, to use this guide most effectively, first skim through the whole thing to see what is there, then start in at the beginning and work through it, again and again, reviewing repeatedly all of the problems and material you've covered so far as you go on to what you are working on currently in class and on the homework and for the upcoming exam(s). Don't be afraid to solve problems more than once,

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